TREATMENT OF DIGITAL CONTROL SYSTEMS AND NUMERICAL PROCESSES IN THE FREQUENCY DOMAIN
MASSACHUSETTS INST OF TECH CAMBRIDGE DIGITAL COMPUTER LAB
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Methods developed for frequency analysis and synthesis of digital computer programs describable in the form of a linear difference equation with constant coefficients. Theorems on the realizability and stability of program transfer functions are developed, and the amplitude, phase, and locus of a program are defined. The adaptation of the methods of analog filters to digital ones is direct, although significant modification may be required. Computer programs can be synthesized along lines employed for networks. Various methods of programing are developed and compared on the basis of time and storage requirements. Criteria are given for choosing the optimum programing procedure by considering the form of the program transfer function. Examples are given of program analysis and synthesis, and one example of synthesizing a program for the compensation of a control system is worked out. Application of the methods to various problems in numerical analysis is shown. The problems of convergence stability and of truncation errors approximation can be analyzed in the frequency domain effectively. The study of conformal mapping is related to the usual methods. A novel way of estimating truncation error is shown. This numerical process is applicable to the given function only when this function can be described by its frequency spectrum.
- Computer Programming and Software